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WI Bourbon France saw British embroilment in the colonial rebellion less as a chance for direct revenge and more a chance to make unilateral gains of enduring importance for France? Specifically, from 1775 Britain's distraction gets the wheels of French Ministers spinning thinking of possible ways to wring a French advantage out of the situation. An additional bonus of the situation is Britain's lack of continental allies.

A party emerges advocating French expansion in Europe during Britain's embroilment. In terms of selecting the target, the formula that eventually emerges from the royal advisors is for a move to annex the Austrian Netherlands, as the course most likely to increase the real power of France and the revenues of the French treasury. More expansive or broader potential designs in Italy or Germany are rejected as being too likely to cause war with a coalition of continental powers. Likewise, France does not commit itself to overseas designs that would make war with Britain inevitable.

In accordance with these designs on southern Netherlands, limited military preparations are made in late 1775 to mid 1776 to ready the army for a campaign.

There is no full or irreversible commitment made however, until after the rebellious colonies declare independence and the British campaign against New York City begins in July 1776. That convinces some fence-sitting decisionmakers that Britain and its colonies are in for a protracted period of fighting.

Preparations are kicked into high gear for an autumn campaign, along with diplomatic preparations.

The French march in September. How quickly could the French military of the day occupy Belgium, and reduce any resisting forts to submission. Would towns, forts and Austrian garrisons resist.

This is a betrayal of the Austrian ally. But what position is Austria in to effectively oppose the move? Belgium is a distant possession of theirs. I would think that though this would be seen as a land-grab like as bold as Frederick's seizure of Silesia in 1740, this would not be enough to excite a pan-European coalition against France. France could also try to offer Austria suitable compensation to allow it to save face.

Is Prussia under the aging and tiring Frederick going to see Belgium as its problem? The Dutch Republic will see this as a problem and a long-term threat, but has no unilateral capacity to oppose French moves. What do the Russians think?

French annexation of Belgium (including Antwerp) is a nightmare for Britain, but how does Britain prioritize from autumn 1776 on?

Does Britain stay at peace with France while trying to hasten an end to the American rebellion by force?

Or does Britain declare war on France and intervene in the Austrian Netherlands, rerouting its Hessian recruits to fight there instead of America, while going into an immediate slowdown of operations in America and attempts to negotiate a settlement with the Americans? Does Britain seek to recruit continental allies, and how would that go?

In the latter situation, Austria as the attacked party seems to be the most natural partner for Britain in opposing France, but it also seems like an Austro-British coalition at this point would be a coalition of losers who could not help each other much and be checkmated by an opposing coalition of France, Prussia, Russia and the American colonists.

So, does France end up annexing Belgium and holding it thereafter?
Is American independence recognized early?
Both? Neither?

If France only wants to do the Belgium thing and not get overtly involved with the Americans, could Britain and France reach a tacit agreement to stay out of each other's wars, or would Britain veto this? In the latter case, how could the French most effectively allocate their resources among their continental and overseas fronts? Is their fleet able to protect their forces in Belgium and the channel, and slip out to American waters, or is the French fleet still not capable of achieving the breakout it achieved in OTL 1778?
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